Abstract
Characterizing infectivity as a function of pathogen dose is integral to microbial risk assessment. Dose-response experiments usually administer doses to subjects at one time. Phenomenological models of the resulting data, such as the exponential and the Beta-Poisson models, ignore dose timing and assume independent risks from each pathogen. Real world exposure to pathogens, however, is a sequence of discrete events where concurrent or prior pathogen arrival affects the capacity of immune effectors to engage and kill newly arriving pathogens. We model immune effector and pathogen interactions during the period before infection becomes established in order to capture the dynamics generating dose timing effects. Model analysis reveals an inverse relationship between the time over which exposures accumulate and the risk of infection. Data from one time dose experiments will thus overestimate per pathogen infection risks of real world exposures. For instance, fitting our model to one time dosing data reveals a risk of 0.66 from 313 Cryptosporidium parvum pathogens. When the temporal exposure window is increased 100-fold using the same parameters fitted by our model to the one time dose data, the risk of infection is reduced to 0.09. Confirmation of this risk prediction requires data from experiments administering doses with different timings. Our model demonstrates that dose timing could markedly alter the risks generated by airborne versus fomite transmitted pathogens.